Religious rites were performed over the dead by the Rev. Mr. Hawley and Mr. Butler, of the Episcopal Church, and Mr. Laurie, of the Presbyterian Church, before leaving the President’s House. The bodies were then hearsed, and the procession led off by the military companies, which filled the avenue in front of the President’s house. The military array, composed of horse, infantry, and artillery, made a very imposing appearance; and the train of carriages which followed extended along the avenue more than a mile. A vast multitude, on foot and on horseback, from the neighboring cities and adjoining country, filled the spaces not occupied by the procession. The whole distance between the President’s and the Capitol square, as far as the vision could reach through the darkness of the day and the dust, seemed to be a living current, in slow movement to the wailing and mournful music of the band, which, with the sound of distant cannon and solemn-pealing bells, alone broke the silence. The immense crowd was perfectly mute in its march. The dread quiet that reigned over all; the almost twilight darkness that dimmed the whole day; the deep mists that shadowed the surrounding hills and horizon from sight; the cloud of dust that covered the long and gloomy procession; the sweeping trains of crape that blackened the closed windows and doors of the dwellings on the way,--gave, altogether, the most saddened and impressive aspect of wo ever worn by this city. It was rendered the more deeply affecting by the contrast of but a few days before, when the warmth of a vernal sun had shone out, giving light and gayety to our streets, opening the buds upon the trees and bringing out the tender green upon the grounds whereon the snow had so recently lain.